All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is
Multiply both sides by r :
Subtract the latter sum from the first, which eliminates all but the first and last terms:
Solve for :
Then as gets arbitrarily large, the term will converge to 0, leaving us with
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
Answer:
50 i - 41
Step-by-step explanation:
Simplify the following:
(-7 i + 8) (i - 6)
(8 - 7 i) (i - 6) = (8) (-6) + (8) (i) + (-7 i) (-6) + (-7 i) (i):
-6×8 + 8 i - 6 (-7 i) - 7 i×i
-6×8 = -48:
-48 + 8 i - 7 i (-6) - 7 i×i
-7 (-6) = 42:
-48 + 8 i + 42 i - 7 i×i
-7 i×i = -7 i^2:
-48 + 8 i + 42 i + -7 i^2
i^2 = -1:
-48 + 8 i + 42 i - 7-1
-7 (-1) = 7:
-48 + 8 i + 42 i + 7
-48 + 8 i + 42 i + 7 = (8 i + 42 i) + (7 - 48) = -41 + 50 i:
Answer: 50 i - 41
You have -4,-3,-2, that is a 3 out of a total of 21 points or numbers on the number line. 3/21 is reduces to 1/7.
3 goes into 21 , 7 times. That is why it reduces to 1/7.
Answer: x = 13
Step-by-step explanation:
8x + 2 = 14x - 76
78 = 6x
x = 13
The first thing we are going to do for this case is define variables.
We have then:
y = the cost of the box
x = one side of the square base
z = height of the box
The volume of the building is 14,000 cubic feet:
x ^ 2 * z = 14000
We cleared z:
z = (14000 / x ^ 2)
On the other hand, the cost will be:
floor = 4 (x ^ 2)
roof = 3 (x ^ 2)
for the walls:
1 side = 16 (x * (14000 / x ^ 2)) = 16 (14000 / x)
4 sides = 64 (14000 / x) = 896000 / x
The total cost is:
y = floor + roof + walls
y = 4 (x ^ 2) + 3 (x ^ 2) + 896000 / x
y = 7 (x ^ 2) + 896000 / x
We derive the function:
y '= 14x - 896000 / x ^ 2
We match zero:
0 = 14x - 896000 / x ^ 2
We clear x:
14x = 896000 / x ^ 2
x ^ 3 = 896000/14
x = (896000/14) ^ (1/3)
x = 40
min cost (y) occurs when x = 40 ft
Then,
y = 7 * (40 ^ 2) + 896000/40
y = 33600 $
Then the height
z = 14000/40 ^ 2 = 8.75 ft
The price is:
floor = 4 * (40 ^ 2) = 6400
roof = 3 * (40 ^ 2) = 4800
walls = 16 * 4 * (40 * 8.75) = 22400
Total cost = $ 33600 (as calculated previously)
Answer:
The dimensions for minimum cost are:
40 * 40 * 8.75
